If f(x) = 1 + x 1 - x , then f(x) is - Vidyadip

MCQ

If $f(x) = \log \frac{{1 + x}}{{1 - x}}$, then $f(x)$ is

A
Even function
B
$f({x_1})f({x_2}) = f({x_1} + {x_2})$
C
$\frac{{f({x_1})}}{{f({x_2})}} = f({x_1} - {x_2})$
✓
Odd function

✓

Answer

Correct option: D.

Odd function

d
(d) Here, $f(x) = \log \left( {\frac{{1 + x}}{{1 - x}}} \right)$

and $f( - x) = \log \left( {\frac{{1 - x}}{{1 + x}}} \right) = \log {\left( {\frac{{1 + x}}{{1 - x}}} \right)^{ - 1}}$

$ = - \log \left( {\frac{{1 + x}}{{1 - x}}} \right) = - f(x)$ ==> $f(x)$ is an odd function.

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